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Table 2 Results on modularity optimization

From: Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

Graph Size [25] EO [26] GSOa EvoGSOb
Karate 34 0.3810/2 \({0.4188}\)*/4 0.4198/4 0.4198/4
Jazz 198 0.4379/4 0.4452/5 \({0.4451}\)*/4 \({0.4451}\)*/4
C.elegans 453 0.4001/10 \({0.4342}\)*/12 0.4304/8 0.4418/11
E-mail 1133 0.4796/13 0.5738/15 0.5275/8 \({0.5655}\)*/15
  1. We report the maximum modularity value Q and the corresponding number of communities Ncoms in the form of (Q/Ncoms)
  2. The best and the second best results are denoted in italic and asterisk, respectively
  3. aConfiguration: batch size = 256, initial \(\tau\) = 0.5, final \(\tau\) = 0.1, learning rate = 0.01, instance = 10
  4. bConfiguration: batch size = 256, initial \(\tau\) = 0.5, final \(\tau\) = 0.1, learning rate = 0.01, instance = 10, cycle \(T_1\) = 100, cycle \(T_2\) = 5000, substitution ratio 1/u = 1/8, mutation rate m = 0.001, and elite ratio = 0.0625